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It is very interesting how the other fermions form a equivalent frozen core in the BCS-ansatz without core for crossover.  This becomes more obvious after previous few weeks, the k-distribution is very much like the Fermi sea for the Fermi gas.  And the inner part is just like a frozen core.  We are trying to look into the simplist case where there is only two pairs. But in this case, the other pair's k-distribution spreads and this hardly looks like a frozen core.  